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ENCIT 2018
Brazilian Congress of Thermal Sciences and Engineering
Performance of Finite Volume Discretization Schemes for the Convective-Diffusive Linear Transport Equation. Part I: Low Eigenvalue-Peclet Ratios.
Submission Author:
Adyllyson Nascimento , SP
Co-Authors:
Adyllyson Nascimento, Gustavo Silva Rodrigues, José Ricardo Figueiredo
Presenter: Adyllyson Nascimento
doi://10.26678/ABCM.ENCIT2018.CIT18-0139
Abstract
Various numerical aspects of several discretization schemes are evaluated by using the two-dimensional transport problem of a scalar property in uniform flow. This problem is modeled by the convective-diffuse transport equation, here discretized by the finite volume method. It is proposed a methodology that evaluates the Peclet number's influence and the dependence on the angle between flow and grid lines on the rms error of the numerical schemes: central differencing, upwind, simple exponential, second order upwind, QUICK, LOADS and UNIFAES. The discretization-generated algebraic system is solved by the ADI method for the five-node schemes. However, the source terms of UNIFAES and LOADS are computed explicitly. The boundary conditions are of the Dirichlet type. The scalar property's values at the domain boundary are provided by analytical solutions. Schemes that employ the generating equation's source term, i.e. UNIFAES and LOADS, present the best performance in nearly all functions, alongside the QUICK scheme. UNIFAES shows the lowest dependence with the flow direction. With the increase of the Peclet number, UNIFAES and QUICK outperform the others, being closely followed by LOADS. However, UNIFAES has the advantage of being unconditionally stable for all Peclet numbers, while QUICK may show wiggly behavior.
Keywords
Numerical Methods, Finite Volumes, Finite Differences, UNIFAES, CFD
